Mathematics

Classification Cramer-Rao bounds on stock price prediction

Article Abstract:

An innovative approach to quantifying the classification Cramer-Rao lower bound, which involves a performance metric for a classifier given input features, is developed. It combines the concepts of sufficient statistics and data compression with a metric that measures class discrimination. The approach allows the assessment of the degree of performance optimality attained by each classifier as it assigns a quantity called the optimality score that indicates the extent of a classifier's approximation of the Bayes classifier. Its potency is demonstrated with two-class prediction problems.

The increasingly common practice of judgmental revision of sales forecasts is analyzed for an industrial company through six quarters and some 900 products. The error distributions in forecasts after managers' revisions are compared to those without revision, using Kolmogorov-Smirnov, medians and t tests. However, it is concluded that non-revised forecasts generally have lesser errors than revised ones and that harmonization between the two types is the best result one can achieve. Revision also improves forecast accuracy but is insignificant where variability is concerned.

Prediction in the one-way error component model with serial correlation

Article Abstract:

The best linear unbiased predictor is formulated for a one-way error component model with serial correlation. It can be easily computed from the GLS estimates and residuals through the use of a transformation, and is applicable to panel data cases which utilize the error component specification and exhibit serial correlation in the remainder disturbance term. This model is then analyzed wherein the remainder disturbances follow either an AR(1), an AR(2), an MA(1) or a special AR(4) process for quarterly data.